Related papers: The overlap in glassy systems
The aim of this review paper is to give a panoramic of the impact of spin glass theory and statistical physics in the study of the K-sat problem. The introduction of spin glass theory in the study of the random K-sat problem has indeed left…
The aim of this work is to prove that it is possible to realise an optical system which produces as output a light intensity that can be expressed in the same mathematical form of the spin glass Hamiltonian. The optical system under study…
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
We study theoretically and numerically a family of multi-point dynamic susceptibilities that quantify the strength and characteristic lengthscales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments…
We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…
We investigate the low temperature phase of three-dimensional Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed value $Q$ of the overlap the model fulfills the clustering property: the connected correlation…
We examine a family of discrete probability distributions that describes the "spillage number" in the extended balls-in-bins model. The spillage number is defined as the number of balls that occupy their bins minus the total number of…
We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles…
We study the fluctuation problems at high temperature in the general mixed $p$-spin glass models under the weak external field assumption: $h= \rho N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster expansion approach…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
We prove a new hypothesis on the conditional distribution of the sample mean of the fluctuations of an i.i.d. random potential in the Anderson model. The paper extends to uniform probability distribution some earlier work with Gaussian…
This is a commentary on two recent experimental papers in PNAS by Vivek et al. and Illing et al. that convincingly address an issue at the junction of two fundamental questions in glass physics: the role of the dimensionality of space on…
Typical features of glass phenomenology such as the Vogel-Fulcher law, the Kauzmann paradox and the Adam-Gibbs relationship are shown to follow from the recently discovered mapping of glasses to Ising spin glasses in a magnetic field. There…
We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…
Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This…
Mixing theoretical topological structures with cutting-edge simulation methods, a recent study in Nature Communications has finally confirmed the existence of topological defects in glasses and their crucial role for plasticity.
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lipschitz with respect to the disorder through a variational…
We use computer simulations to investigate the static properties of a simple glass-forming fluid in which the positions of a finite fraction of the particles has been frozen in. By probing the equilibrium distribution of the overlap between…